How do you unclog a drain in the bathroom sink?

Remove as much as possible with a snake or drain cleaning tool. Pour ½ cup baking soda then ½ cup white vinegar in the drain and cover, letting sit for 20 minutes. Boil water, remove cover, and pour water down the drain. You may have to repeat the process.

Try a cup of Vinegar and a tea kettle full of boiling water. I take a cup of plain ordinary white vinegar pour that down the drain followed right away by the tea kettle of boiling water it works for me no problem. My plumber taught me this trick.

After you've cleaned out the drain with a snake (dollar tree) and run hot water, if its still going too slow, I clean out the traps.... https://www.youtube.com/watch?v=hySkwXMn0pA&t=44s be sure to put a plastic tub/tray underneath on the cabinet shelf to catch the dirty water.

Buy a liquid drain cleaner. At bedtime pour a good amount of this chemical into the drain. Leave it overnight. First thing in the morning slowly start running water down the drain. If it's not totally unblocked, repeat the next night. I've never had to repeat this more than one time and that has been a rarity.

There is a tool I use (mine was called a hair grabber) that you push down the drain. It is long, flexible and has little barbs that stick out. My problem has always been hair that goes down the drain, gets trapped and then soap and other gunk gets caught on it. Work the grabber down your drain and then after wiggling it arond, pull it back up. You will be amazed at the gunk. Once it's all cleaned out, run some Dawn dish detergent and hot water down it. Do this occasionally and you won't have a problem. It works on the tub drain too, although I had to unscrew my drain cover to do it on mine.